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Stokes flow in a two-dimensional micro-device combined by a cross-slot and a microfluidic four-roll mill

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Abstract

The flow structures in a novel microfluidics device (CS-MFRM) combining a cross-slot (CS) and a microfluidics four-roll mill (MFRM) have been investigated through a two-dimensional boundary element method. By changing the volume flow rates at various inlets of a CS-MFRM, diverse flow structures can be generated. Some of them are proposed to be employed to achieve some functions in the fabrication process of anisotropic particles. The stagnant points and eddies in those flows are particularly discussed since they are critical to trap and/or rotate droplets. Energy consumption of eddies generated in branches in some flow structures is also investigated in this paper.

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Abbreviations

μ :

The viscosity of continuous phase

λ :

The viscosity ratio of the droplet to the continuous phase

G :

Shear rate

p :

Pressure

u :

Velocity vector

f :

Surface stress

S ij :

Fundamental solution of the two-dimensional Stokes equations

T ijk :

Associated stress kernel of the fundamental solution

Q :

Volume flow rate in a channel

w 0 :

Half width of a channel

r c :

Radius of central circular cavity

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Authors and Affiliations

  1. School of Science, Tianjin University, Tianjin, 300072, People’s Republic of China

    Jing Guan

  2. School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, People’s Republic of China

    Jinxia Liu, Xiaoduan Li, Jun Tao & Jingtao Wang

  3. State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin, People’s Republic of China

    Jingtao Wang

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  1. Jing Guan
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  2. Jinxia Liu
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  3. Xiaoduan Li
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  4. Jun Tao
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  5. Jingtao Wang
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Correspondence to Jingtao Wang.

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Guan, J., Liu, J., Li, X. et al. Stokes flow in a two-dimensional micro-device combined by a cross-slot and a microfluidic four-roll mill. Z. Angew. Math. Phys. 66, 149–169 (2015). https://doi.org/10.1007/s00033-013-0396-z

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  • DOI: https://doi.org/10.1007/s00033-013-0396-z

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